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<b>let </b><font color="Maroon" title="c1">C</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="altcat_1.html#L2" title="ALTCAT_1:struct.2">AltCatStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">O</font>, <font color="Olive" title="b2">A</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font><br/> for <font color="Olive" title="b3">M</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">O</font>,<font color="Olive" title="b2">A</font>  st <font color="Olive" title="b1">O</font> is <a href="altcat_3.html#V7" title="ALTCAT_3:attr.7">terminal</a> holds <br/><font color="Olive" title="b3">M</font> is <a href="altcat_3.html#V4" title="ALTCAT_3:attr.4">mono</a></span><br/><b>let </b><font color="Maroon" title="c2">O</font>, <font color="Maroon" title="c3">A</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">M</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c3">A</font>  st <font color="Maroon" title="c2">O</font> is <a href="altcat_3.html#V7" title="ALTCAT_3:attr.7">terminal</a> holds <br/><font color="Olive" title="b1">M</font> is <a href="altcat_3.html#V4" title="ALTCAT_3:attr.4">mono</a></span><br/><b>let </b><font color="Maroon" title="c4">M</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c3">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">O</font> is <a href="altcat_3.html#V7" title="ALTCAT_3:attr.7">terminal</a> implies <font color="Maroon" title="c4">M</font> is <a href="altcat_3.html#V4" title="ALTCAT_3:attr.4">mono</a> )</span><br/>





<b>assume </b><a NAME="E1:11"/><i><font color="Green" title="E5">A1</font></i>: 
<font color="Maroon" title="c2">O</font> is <a href="altcat_3.html#V7" title="ALTCAT_3:attr.7">terminal</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">M</font> is <a href="altcat_3.html#V4" title="ALTCAT_3:attr.4">mono</a></span><br/>

<b>let </b><font color="Maroon" title="c5">o</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_3.html#D7" title="ALTCAT_3:def.7">ALTCAT_3:def 7</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c2">O</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="subset_1.html#M1" title="SUBSET_1:mode.1">M2</a>(<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c2">O</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>)  holds <br/>(  not <font color="Maroon" title="c4">M</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">M</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Olive">b<sub>2</sub></font> or <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> ) )</span><br/>

<b>assume </b><a NAME="E2:11"/><i><font color="Green" title="E6">A2</font></i>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c2">O</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="subset_1.html#M1" title="SUBSET_1:mode.1">M2</a>(<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c2">O</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>)  holds <br/>(  not <font color="Maroon" title="c4">M</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">M</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Olive">b<sub>2</sub></font> or <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> )</span><br/>

<b>let </b><font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c7">b</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c2">O</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">M</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">M</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c7">b</font> or <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font> )</span><br/>

<b>assume </b><a NAME="E3:11"/>
<font color="Maroon" title="c4">M</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">M</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c7">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b</font></span><br/>

<b>consider </b><font color="Maroon" title="c8">N</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c2">O</font><b> such that </b><br/><a NAME="E5:11"/>
<font color="Maroon" title="c8">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c2">O</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span>
 <b>and </b><br/><a NAME="E6:11"/><i><font color="Green" title="E7">A3</font></i>: 
for <font color="Olive" title="b1">M1</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c2">O</font>  st <font color="Olive" title="b1">M1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c2">O</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> holds <br/><font color="Maroon" title="c8">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">M1</font>
 <b>by </b><i><a class="txt" href="#E1:11"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="altcat_3.html#T27" title="ALTCAT_3:th.27">ALTCAT_3:27</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c6">a</font> = 
<font color="Maroon" title="c8">N</font>
<b>by </b><i><a class="txt" href="#E2:11"><i><font color="Green" title="E6">A2</font></i></a>, <a class="txt" href="#E6:11"><i><font color="Green" title="E7">A3</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c7">b</font>
<b>by </b><i><a class="txt" href="#E2:11"><i><font color="Green" title="E6">A2</font></i></a>, <a class="txt" href="#E6:11"><i><font color="Green" title="E7">A3</font></i></a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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